A Mixed Frequency Stochastic Volatility Model for Intraday Stock Market Returns

We propose a mixed frequency stochastic volatility (MFSV) model for the dynamics of intraday asset return volatility. In order to account for long-memory we separate stochastic daily and intraday volatility patterns by introducing a long-run component that changes at daily frequency and a short-run component that captures the remaining intraday volatility dynamics. An additional component captures deterministic intraday patterns. We analyze the stochastic properties of the resulting non-linear state-space model both on the daily and the intraday frequency and show how the model can be estimated in a single step using simulated maximum likelihood based on Efficient Importance Sampling (EIS). We apply the model to intraday returns of five New York Stock Exchange traded stocks. The estimation results indicate distinct dynamic patterns for daily and intradaily volatility components, where about 50% of intraday volatility dynamics are explained by the daily component. In-sample diagnostic tests and an out-of-sample forecasting experiment indicate that already the very basic model specification successfully accounts for the complex dynamic and distributional properties of asset returns both on the intraday and the daily frequency